What are the solutions to the equation solvefor x,x^2=2x+1 ?

The solutions to the equation solvefor x,x^2=2x+1 are x=1+sqrt(2),x=1-sqrt(2)

Find the zeros of solvefor x,x^2=2x+1

The zeros of solvefor x,x^2=2x+1 are x=1+sqrt(2),x=1-sqrt(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x, x^{2} = 2 x + 1

x = 1 + 2, x = 1 - 2

Decimal Notation

x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

x^{2} = 2 x + 1

Move

1

to the left side

x^{2} - 1 = 2 x

Move

2 x

to the left side

x^{2} - 1 - 2 x = 0

Write in the standard form

a x^{2} + b x + c = 0

x^{2} - 2 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot (- 1) = 22

x_{1, 2} = \frac{- ( - 2 ) \pm 2 2}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 2}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 2 2}{2 \cdot 1}

x = \frac{- ( - 2 ) + 2 2}{2 \cdot 1} : 1 + 2

x = \frac{- ( - 2 ) - 2 2}{2 \cdot 1} : 1 - 2

The solutions to the quadratic equation are:

x = 1 + 2, x = 1 - 2

x^{2} + 7 x - 1 = 0

y^{2} - 14 y + 49 = 0

- x^{2} + 78 x + 460 = 1581

5 + 5 x^{2} - 2 x = 3 x^{2} - 4

3 x^{2} - 4 x - 11 = 0

What are the solutions to the equation solvefor x,x^2=2x+1 ?
The solutions to the equation solvefor x,x^2=2x+1 are x=1+sqrt(2),x=1-sqrt(2)
Find the zeros of solvefor x,x^2=2x+1
The zeros of solvefor x,x^2=2x+1 are x=1+sqrt(2),x=1-sqrt(2)